R/Ii.R

In integIRTy: Integrating Multiple Modalities of High Throughput Assays Using Item Response Theory

Ii <-
function (th, it, D = 1) 
{
    pr <- Pi(th, it, D = D)
    P <- pr$Pi
    Q <- 1 - P
    dP <- pr$dPi
    d2P <- pr$d2Pi
    d3P <- pr$d3Pi
    Ii <- dP^2/(P * Q)
    dIi <- dP * (2 * P * Q * d2P - dP^2 * (Q - P))/(P^2 * Q^2)
    d2Ii <- (2 * P * Q * (d2P^2 + dP * d3P) - 2 * dP^2 * d2P * 
        (Q - P))/(P^2 * Q^2) - (3 * P^2 * Q * dP^2 * d2P - P * 
        dP^4 * (2 * Q - P))/(P^4 * Q^2) + (3 * P * Q^2 * dP^2 * 
        d2P - Q * dP^4 * (Q - 2 * P))/(P^2 * Q^4)
    res <- list(Ii = Ii, dIi = dIi, d2Ii = d2Ii)
    return(res)
}